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      SUBROUTINE <a name="CUNMRQ.1"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a>( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
     $                   WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CUNMRQ.20"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a> overwrites the general complex M-by-N matrix C with
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                  SIDE = 'L'     SIDE = 'R'
</span><span class="comment">*</span><span class="comment">  TRANS = 'N':      Q * C          C * Q
</span><span class="comment">*</span><span class="comment">  TRANS = 'C':      Q**H * C       C * Q**H
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where Q is a complex unitary matrix defined as the product of k
</span><span class="comment">*</span><span class="comment">  elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Q = H(1)' H(2)' . . . H(k)'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  as returned by <a name="CGERQF.31"></a><a href="cgerqf.f.html#CGERQF.1">CGERQF</a>. Q is of order M if SIDE = 'L' and of order N
</span><span class="comment">*</span><span class="comment">  if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SIDE    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'L': apply Q or Q**H from the Left;
</span><span class="comment">*</span><span class="comment">          = 'R': apply Q or Q**H from the Right.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  No transpose, apply Q;
</span><span class="comment">*</span><span class="comment">          = 'C':  Transpose, apply Q**H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix C. M &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix C. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  K       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of elementary reflectors whose product defines
</span><span class="comment">*</span><span class="comment">          the matrix Q.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', M &gt;= K &gt;= 0;
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', N &gt;= K &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) COMPLEX array, dimension
</span><span class="comment">*</span><span class="comment">                               (LDA,M) if SIDE = 'L',
</span><span class="comment">*</span><span class="comment">                               (LDA,N) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">          The i-th row must contain the vector which defines the
</span><span class="comment">*</span><span class="comment">          elementary reflector H(i), for i = 1,2,...,k, as returned by
</span><span class="comment">*</span><span class="comment">          <a name="CGERQF.62"></a><a href="cgerqf.f.html#CGERQF.1">CGERQF</a> in the last k rows of its array argument A.
</span><span class="comment">*</span><span class="comment">          A is modified by the routine but restored on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A. LDA &gt;= max(1,K).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (input) COMPLEX array, dimension (K)
</span><span class="comment">*</span><span class="comment">          TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment">          reflector H(i), as returned by <a name="CGERQF.70"></a><a href="cgerqf.f.html#CGERQF.1">CGERQF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) COMPLEX array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment">          On entry, the M-by-N matrix C.
</span><span class="comment">*</span><span class="comment">          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array C. LDC &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment">          If SIDE = 'L', LWORK &gt;= max(1,N);
</span><span class="comment">*</span><span class="comment">          if SIDE = 'R', LWORK &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">          For optimum performance LWORK &gt;= N*NB if SIDE = 'L', and
</span><span class="comment">*</span><span class="comment">          LWORK &gt;= M*NB if SIDE = 'R', where NB is the optimal
</span><span class="comment">*</span><span class="comment">          blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.93"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      INTEGER            NBMAX, LDT
      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I, I1, I2, I3, IB, IINFO, IWS, LDWORK, LWKOPT,
     $                   MI, NB, NBMIN, NI, NQ, NW
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      COMPLEX            T( LDT, NBMAX )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.115"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.116"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
      EXTERNAL           <a name="LSAME.117"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.117"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CLARFB.120"></a><a href="clarfb.f.html#CLARFB.1">CLARFB</a>, <a name="CLARFT.120"></a><a href="clarft.f.html#CLARFT.1">CLARFT</a>, <a name="CUNMR2.120"></a><a href="cunmr2.f.html#CUNMR2.1">CUNMR2</a>, <a name="XERBLA.120"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      LEFT = <a name="LSAME.130"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> )
      NOTRAN = <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
      LQUERY = ( LWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     NQ is the order of Q and NW is the minimum dimension of WORK
</span><span class="comment">*</span><span class="comment">
</span>      IF( LEFT ) THEN
         NQ = M
         NW = MAX( 1, N )
      ELSE
         NQ = N
         NW = MAX( 1, M )
      END IF
      IF( .NOT.LEFT .AND. .NOT.<a name="LSAME.143"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.145"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'C'</span> ) ) THEN
         INFO = -2
      ELSE IF( M.LT.0 ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
         INFO = -7
      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -10
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( M.EQ.0 .OR. N.EQ.0 ) THEN
            LWKOPT = 1
         ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Determine the block size.  NB may be at most NBMAX, where
</span><span class="comment">*</span><span class="comment">           NBMAX is used to define the local array T.
</span><span class="comment">*</span><span class="comment">
</span>            NB = MIN( NBMAX, <a name="ILAENV.167"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 1, <span class="string">'<a name="CUNMRQ.167"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a>'</span>, SIDE // TRANS, M, N,
     $                               K, -1 ) )
            LWKOPT = NW*NB
         END IF
         WORK( 1 ) = LWKOPT
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
            INFO = -12
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.179"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CUNMRQ.179"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span>      NBMIN = 2
      LDWORK = NW
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
         IWS = NW*NB
         IF( LWORK.LT.IWS ) THEN
            NB = LWORK / LDWORK
            NBMIN = MAX( 2, <a name="ILAENV.197"></a><a href="ilaenv.f.html#ILAENV.1">ILAENV</a>( 2, <span class="string">'<a name="CUNMRQ.197"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a>'</span>, SIDE // TRANS, M, N, K,
     $              -1 ) )
         END IF
      ELSE
         IWS = NW
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use unblocked code
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="CUNMR2.208"></a><a href="cunmr2.f.html#CUNMR2.1">CUNMR2</a>( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
     $                IINFO )
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Use blocked code
</span><span class="comment">*</span><span class="comment">
</span>         IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
     $       ( .NOT.LEFT .AND. NOTRAN ) ) THEN
            I1 = 1
            I2 = K
            I3 = NB
         ELSE
            I1 = ( ( K-1 ) / NB )*NB + 1
            I2 = 1
            I3 = -NB
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( LEFT ) THEN
            NI = N
         ELSE
            MI = M
         END IF
<span class="comment">*</span><span class="comment">
</span>         IF( NOTRAN ) THEN
            TRANST = <span class="string">'C'</span>
         ELSE
            TRANST = <span class="string">'N'</span>
         END IF
<span class="comment">*</span><span class="comment">
</span>         DO 10 I = I1, I2, I3
            IB = MIN( NB, K-I+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Form the triangular factor of the block reflector
</span><span class="comment">*</span><span class="comment">           H = H(i+ib-1) . . . H(i+1) H(i)
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="CLARFT.243"></a><a href="clarft.f.html#CLARFT.1">CLARFT</a>( <span class="string">'Backward'</span>, <span class="string">'Rowwise'</span>, NQ-K+I+IB-1, IB,
     $                   A( I, 1 ), LDA, TAU( I ), T, LDT )
            IF( LEFT ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              H or H' is applied to C(1:m-k+i+ib-1,1:n)
</span><span class="comment">*</span><span class="comment">
</span>               MI = M - K + I + IB - 1
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              H or H' is applied to C(1:m,1:n-k+i+ib-1)
</span><span class="comment">*</span><span class="comment">
</span>               NI = N - K + I + IB - 1
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Apply H or H'
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="CLARFB.259"></a><a href="clarfb.f.html#CLARFB.1">CLARFB</a>( SIDE, TRANST, <span class="string">'Backward'</span>, <span class="string">'Rowwise'</span>, MI, NI,
     $                   IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
     $                   LDWORK )
   10    CONTINUE
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CUNMRQ.267"></a><a href="cunmrq.f.html#CUNMRQ.1">CUNMRQ</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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